Earth Maiden Arjuna (or Earth Girl Arjuna): This has so many
excellent aspects to it that it's a pity its environmental message
turns people off. It has great secondary characters (including one who
gets both excellent lines and an entire episode that was apparently so
controversial that it couldn't be aired on TV), beautiful character
focused episodes, and it never shies away from showing just how
difficult and isolating it is for the heroine to be so strongly
environmentally aware; it never pitches its environmental message as
at all easy. (And I love the music without reservation because it hits
my buttons just right.)

It has always amazed me that Arjuna was actually licensed in the US,
partly because of the environmental message and partly because it's
so much a subtle character drama instead of anything more active (yes,
despite the periodic quite nice action scenes).

By the way, Arjuna is a Shoji Kawamori project. (Yes, I'm
trying to get you to give it a chance.)

Shingu: Secret of the Stellar Wars: This is an excellent show,
as plenty of people will correctly tell you. I had some reactions when I finally saw it.

Alien Nine: I'm not sure that this is a good show as such (for a
start it doesn't so much end as stop abruptly in the middle of
something). What makes it so memorable is that it's so harrowing once
you start paying attention and it's chock-full of interestingly weird
science-fiction concepts (especially for alien creatures). You can read
more about it here and also see Scamp's
longer writeup.

Ordinarily memorable:

Animation Runner Kuromi: This is a very interesting and apparently
extremely true to life look inside the anime production process.
It's also touching, periodically funny, and full of small details.

Read Or Die (OVA): The first OVA is the distilled and turbo-charged
essence of a particular kind of wild, supernatural action-adventure
show. Crazy things are happening all of the time, one on top of the
other, right from the opening moments. The other two OVAs can't top
it or fully keep up the momentum and so mostly serve to finish off
the story, but this in no way diminishes the sheer impact and momentum
of the first OVA.

(The subsequent TV series is in an entirely different genre.)

Millennium Actress: I'm not as taken with this film as some people
are, but it's still an excellent film. Mind you I've only seen it once;
possibly I should rewatch it.

Honorable mentions:

Cowboy Bebop: The Movie: I'm docking this memorability points because
it was basically a big episode of the TV series. It doesn't stand out
beyond 'hey, a chunk more of Cowboy Bebop'. That's still nice but it's
not really earth-shaking.

Super GALS! Kotobuki Ran: This has frenzied energy and a quirky
charm, but it's possibly a good thing that I only saw part of it;
all 52 episodes might be a bit too much. I'm still amused by how the
theoretically highly rebellious Ran always came down on the side of
propriety when the dust settled.

Things from 2001 that I want to see and am going to real soon now, honest:

Angelic Layer

Figure 17

Noir: This is yet another show that the local anime clubs started
showing just as they started collapsing, so I've only seen a number
of the early episodes.

Popee the Performer: Due to Shinmaru at The Cart Driver.
He inspired me to check out the first episode and yes, it's my kind
of comedy. I just have to watch the rest of it someday.

Things I want to see are here in large part because I expect that when I
see them they'll be good enough to place into at least the ordinarily
memorable section. Some I rather suspect will be standouts.